The circumstances surrounding Kakashi's suspension are kept hushed.
It's politics. The peace treaties Hiruzen painstakingly negotiated between the five Shinobi nations only draw a fragile veneer of peace over the pain and hatred wracking Konoha. It's like laying a spiderweb over a boiling cauldron. Too many people have lost too much to forgive so easily.
Rin's kidnapping was Kiri's last attempt at destroying Konoha, a sneak attack that occurred after a tentative ceasefire. For their breach of ceasefire, the Sandaime managed to wrangle several favourable concessions from Kiri, but letting the masses know of Kiri's plan would only exacerbate anger and unrest. Adding fear of a bijuu attack to that volatile mix of emotions would send everything boiling over.
What happened to Rin was an opportunity and the Sandaime acted nothing less than prudently, but seeing Rin's death being used like that... it left a bitter taste in Sakumo's mouth. As for Rin, well. "It's good, isn't it? At least something useful came of it," she said. It was true, Sakumo supposed, but he was too old to have her relentless optimism.
Hiruzen has to step down after the mass funeral to appease growing anti-Iwa sentiment (anti-any-other-nation sentiment, in truth) and Minato becomes the Yondaime. It does Konoha good despite Danzou's faction's displeasure — there's a new, young leader (handsome at that, with a lovely wife) who is a venerated war veteran famous for wiping out a thousand Iwa-nin in one go.
The citizenry gradually calm down but it puts Kakashi in the spotlight more than ever. He's the only one left of the new Yondaime's students. There's a thin line between fame and infamy, and with Kakashi that line might as well be non-existent.
No-one really knows why Rin died, only that Kakashi killed her.
Friend Killer.
Epithets can make or break you. Some say it with fear, others with derision, but the worst are the ones who say it with twisted sort of admiration.
Friend Killer. A person who would unflinchingly murder his own friend for the sake of Konoha. Sakumo's sins are surely washed away in their minds, now.
Yet that's not true either. They'll hate him for anything and love him for just as little. No one cares about the truth, only scandal and self-justification of what horrors they've committed. Surely they can be forgiven when there's Friend Killer Kakashi, right?
Rin is fury and misery and guilt all rolled up in one whenever she hears the whispering behind Kakashi's back, but Kakashi never gives them the satisfaction of seeing him react. Despite not even being a teenager, his expressionless, half-masked stare is enough to send the rumour-mongers scurrying away by the strength of his reputation alone. But Sakumo sees the truth in the hollowness of his gaze — Kakashi believes that ugly epithet, perhaps even more than those who came up with it.
A/N: Kakashi is around 11 now. There's lots of discreet timeskipping in and between chapters so the timeline is kinda fuzzy, sorry.